LuxRender runs on all versions of Windows since Windows 2000, including XP, Vista and Windows 7, both 32 bit and 64 bit.
Unbiased rendering is very processor intensive, therefore fast processors with multiple cores will work best. However, the program will run on any modern processor.
Please download the right version of LuxRender. The 64 bit version can deal with larger amounts of memory, but only runs on 64 bit versions of Windows. The SSE compatibility version is intended for older systems with Pentium III and Athlon XP processors. If you're not sure which version to choose, the 32 bit version is a safe bet.
The download file consists of a zip file containing a folder. Just move that folder to a convenient locations, for example the Program Files folder.